How many factors?

3 traditional possibilities

Scree Plot (Cattell) - Not a test

Look for bend in plot

Include factor located right at bend point

Kaiser (or Latent Root) criterion

Eigenvalues greater than 1

Also, 1 is the amount of variance accounted for by a single item (r2 = 1.00). If eigenvalue < 1.00 then factor accounts for less variance than a single item.

A priori hypothesized number of factors

Scree Plot (Cattell)

Scree Plot (Cattell’s) method:

Imagine drawing a straight line that summarizes the vertical part of the plot,

and another that summarizes the horizontal part.

The point of inflexion is the data point at which these two lines meet.

Rule-of-thumb:

Retain (extract) the factors to the left of the point of inflexion

Kaiser’s eigenvalue > 1 criterion

Kaiser’s (Latent Root) method:

Eigenvalues greater than 1.

λ= 1.0 is the amount of variance accounted for by a single item (r2 = 1.0).

If λ < 1.0, then factor accounts for less variance than a single item.

Retain (extract) the factors greater than λ = 1.0

Critique

Kaiser’s eigenvalue > 1 criterion (K1; default in SPSS)

Although this rule is the default in SPSS, studies have been unanimous in finding that it is the least accurate guideline available

Zwick and Velicer (1986) “we cannot recommend the K1 rule for PCA [principal component analysis]” (p. 439)

“The eigenvalue greater than one rule was extremely inaccurate and was the most variable of all the methods. Continued use of this method is not recommended” (Velicer, Eaton, & Fava, 2000, p. 68)

Most studies have found that K1 consistently overestimates the true number of components/factors in the population

Various Factor Retention Criteria

”We suggest researchers use a combination of SMT [sequential chi-square model tests] and either Hull, the EKC [empirical Kaiser criterion], or traditional PA [parallel analysis], because the number of factors was almost always correctly retrieved if those methods converged. When the results of this combination rule are inconclusive, traditional PA, CD [comparison data method], and the EKC performed comparatively well.” (Auerswald & Moshagen, 2019, p. 1)

=> These methods should be combined for a more refined analysis

Sequentical Chi-Square Model

Either

Hull

Empirical Kaiser criterion

Traditional parallel analysis

Last changed3 months ago